Electrophoresis of colloidal particles in a salt-free medium

A general theory for the electrophoretic mobility of dilute spherical colloidal particles in a salt-free medium containing counterions only is given. This theory assumes that each particle is surrounded by a spherical free volume, within which electroneutrality as a whole holds. It is shown that the mobility can be obtained from the balance between the Stokes drag for the case where the particle is uncharged and the pressure due to the excess counterion charge on the outer boundary of the free volume. The mobility μμ is thus expressed as μ=Qexp(y(R))/Dμ=Qexp(y(R))/D, where QQ is the particle surface charge, DD is the drag coefficient of the particle when uncharged, and y(R)y(R) is the scaled potential value at the outer boundary of the free volume.